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Shepherd, A. and Ivins, E. and Rignot, E. and Smith, B. and van den Broeke, M. and Velicogna, I. and Whitehouse, P. and Briggs, K. and Joughin, I. and Krinner, G. and Nowicki, S. and Payne, T. and Scambos, T. and Schlegel, N. and Geruo, A. and Agosta, C. and Ahlstrøm, A. and Babonis, G. and Barletta, V. and Blazquez, A. and Bonin, J. and Csatho, B. and Cullather, R. and Felikson, D. and Fettweis, X. and Forsberg, R. and Gallee, H. and Gardner, A. and Gilbert, L. and Groh, A. and Gunter, B. and Hanna, E. and Harig, C. and Helm, V. and Horvath, A. and Horwath, M. and Khan, S. and Kjeldsen, K. and Konrad, H. and Langen, P. and Lecavalier, B. and Loomis, B. and Luthcke, S. and McMillan, M. and Melini, D. and Mernild, S. and Mohajerani, Y. and Moore, P. and Mouginot, J. and Moyano, G. and Muir, A. and Nagler, T. and Nield, G. and Nilsson, J. and Noel, B. and Otosaka, I. and Pattle, M.P. and Peltier, W.R. and Nadege, P. and
Rietbroek, R. and Rott, H. and Sandberg-Sørensen, L. and Sasgen, I. and Save, H. and Schrama, E. and Schroder, L. and Seo, K-W. and Simonsen, S. and Slater, T. and Spada, G. and Sutterley, T. and Talpe, M. and Tarasov, L. and van de Berg, W.J. and van der Wal, W. and van Wessem, M. and Vishwakarma, B.D. and Wiese, D. and Wouters, B. (2018) 'Mass balance of the Antarctic ice sheet from 1992 to 2017.', Nature., 558 (7709). pp. 219-222.
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Mass balance of the Antarctic ice sheet from 1992 to 2017
1
The IMBIE team 2
Andrew Shepherd1,*, Erik Ivins2, Eric Rignot3, Ben Smith4, Michiel van den Broeke5, Isabella 3
Velicogna3, Pippa Whitehouse6, Kate Briggs1, Ian Joughin4, Gerhard Krinner7, Sophie Nowicki8, Tony 4
Payne9, Ted Scambos10, Nicole Schlegel11, Geruo A3, Cécile Agosta12, Andreas Ahlstrøm13, Greg 5
Babonis14, Valentina Barletta15, Alejandro Blazquez16, Jennifer Bonin17, Beata Csatho18, Richard 6
Cullather19, Denis Felikson20, Xavier Fettweis12, Rene Forsberg15, Hubert Gallee21, Alex Gardner11, Lin 7
Gilbert22, Andreas Groh23, Brian Gunter24, Edward Hanna25, Christopher Harig26, Veit Helm27, 8
Alexander Horvath28, Martin Horwath23, Shfaqat Khan15, Kristian K. Kjeldsen29,13, Hannes Konrad1, 9
Peter Langen30, Benoit Lecavalier31, Bryant Loomis8, Scott Luthcke8, Malcolm McMillan1, Daniele 10
Melini32, Sebastian Mernild33,34,35, Yara Mohajerani3, Philip Moore36, Jeremie Mouginot3,21, Gorka 11
Moyano37, Alan Muir22, Thomas Nagler38, Grace Nield6, Johan Nilsson11, Brice Noel5, Ines Otosaka1, 12
Mark E. Pattle37, W. Richard Peltier39, Nadege Pie20, Roelof Rietbroek40, Helmut Rott38, Louise 13
Sandberg-Sørensen15, Ingo Sasgen27, Himanshu Save20, Ernst Schrama41, Ludwig Schröder23, Ki-Weon 14
Seo42, Sebastian Simonsen15, Tom Slater1, Giorgio Spada43, Tyler Sutterley3, Matthieu Talpe10, Lev 15
Tarasov31, Willem Jan van de Berg5, Wouter van der Wal41, Melchior van Wessem5, Bramha Dutt 16
Vishwakarma44, David Wiese11, Bert Wouters5 17
1. University of Leeds; 2. Jet Propulsion Lab; 3. University of California Irvine; 4. University of 18
Washington; 5. Utrecht University; 6. Durham University; 7. CNRS; 8. NASA GSFC; 9. University of 19
Bristol; 10. University of Colorado; 11. NASA JPL; 12. University of Liège; 13. Geological Survey of 20
Denmark and Greenland; 14. State University of New York at Buffalo; 15. DTU Space; 16. LEGOS; 17. 21
University of South Florida; 18. University at Buffalo; 19. NASA GMAO; 20. University of Texas ; 21. 22
University Grenoble Alpes; 22. University College London; 23. Technische Universitat Dresden; 24. 23
Georgia Institute of Technology; 25. University of Lincoln; 26. University of Arizona; 27. AWI 24
Helmholtz Zentrum; 28. Technical University Munich; 29. Natural History Museum of Denmark; 30. 25
Danish Meteorological Institute; 31. Memorial University of Newfoundland; 32. INGV; 33. Nansen 26
Environmental and Remote Sensing Center; 34. Western Norway University of Applied Sciences; 35. 27
Universidad de Magallanes; 36. Newcastle University; 37. isardSAT; 38. ENVEO Gmbh; 39. University 28
of Toronto; 40. University of Bonn; 41. Delft University of Technology; 42. Seoul National University; 29
43. Urbino University; 44. University of Stuttgart 30
*Corresponding author: Andrew Shepherd [email protected]
31
The Antarctic ice sheet is an important indicator of climate change and driver of sea level rise.
32
Here, we combine satellite observations of its changing volume, flow, and gravitational attraction
33
and surface mass balance modelling, to show that it lost 2720 ± 1390 Gt of ice between 1992 and
34
2017 - a 7.6 ± 3.9 mm contribution to mean sea level. Ocean-driven melting has caused rates of ice
35
loss from West Antarctica to rise from 53 ± 29 Gt/yr in the 1990s to 159 ± 26 Gt/yr in the 2010s. Ice
36
shelf collapse has driven Antarctic Peninsula ice loss up from 7 ± 13 Gt/yr in the 1990s to 33 ± 16
37
Gt/yr in the 2010s. We find large variations in and among model estimates of surface mass
38
balance and glacial isostatic adjustment in East Antarctica, and its 25-year mass trend (5 ± 46
39
Gt/yr) is still the least certain.
40
The Antarctic ice sheets hold enough water to raise global sea level by 58 metres 1. They channel ice 41
to the oceans through a network of glaciers and ice streams 2, each with a substantial inland 42
catchment 3. Fluctuations in the grounded ice sheet mass arise due to differences between net snow 43
accumulation at the surface, meltwater runoff, and ice discharge into the ocean. In recent decades, 44
reductions in the thickness 4 and extent 5 of floating ice shelves have disturbed inland ice flow, 45
triggering retreat 6,7, acceleration 8,9, and drawdown 10,11 of many marine terminating ice streams. A 46
variety of techniques have been developed to measure changes in ice sheet mass, based on satellite 47
observations of their speed 12, volume 13, and gravitational attraction 14 combined with modelled 48
surface mass balance 15 and glacial isostatic adjustment16. Since 1989, there have been more than 49
150 assessments of ice loss from Antarctica based on these approaches 17. An inter-comparison of 12 50
such estimates 18, demonstrated that the three principal satellite techniques provide similar results 51
at the continental scale and, when combined, lead to an estimated mass loss of 71 ± 53 Gt of ice per 52
year averaged over the period 1992 to 2011. Here, we extend this assessment to include twice as 53
many studies, doubling the overlap period and extending the record through to 2017. 54
We collated 24 independently-derived estimates of ice sheet mass balance (Figure 1) determined 55
within the period 1992 to 2017 and based upon the techniques of satellite altimetry (7 estimates), 56
gravimetry (15 estimates) or the input-output method (2 estimates). Altogether, there were 24, 24, 57
and 23 individual estimates of mass change computed within defined geographical limits 19,20 for the 58
East Antarctic, West Antarctic and the Antarctic Peninsula ice sheets, respectively. Rates of ice sheet 59
mass change were compared (see Methods) over common intervals of time 18. We then averaged 60
rates of ice sheet mass balance based on the same class of satellite observations to produce three 61
technique-dependent time series of mass change in each geographical region (see Methods). Within 62
each class, the annual mass rate uncertainty was computed as the mean uncertainty of the 63
individual contributions. The final, reconciled estimate of ice sheet mass change for each region was 64
computed as the mean of the technique-dependent values available at each epoch (Figure 1). In 65
computing the associated uncertainty, we assumed that the errors for each technique are 66
independent. To estimate the cumulative mass change and its uncertainty (Figure 2), we integrated 67
the reconciled estimates for each ice sheet and weighted the annual uncertainty by 1/√n, where n is 68
the number of years elapsed relative to the start of each time series. Antarctic ice sheet mass trends 69
and their uncertainties (Table 1) were computed as the linear sum and root sum square of the 70
regional trends and their uncertainties, respectively. 71
The level of disagreement between individual estimates of ice sheet mass balance increases with the 72
area of each ice sheet region, with average per-epoch standard deviations of 11, 21, and 37 Gt/yr at 73
the Antarctic Peninsula, West Antarctica, and East Antarctica, respectively (Figure 1 and Methods). 74
Among the techniques, gravimetric estimates are the most abundant and also the most closely 75
aligned, though their spread increases in East Antarctica where glacial isostatic adjustment remains 76
poorly constrained 21 and is least certain when spatially integrated 22-33 due to the region’s vast 77
extent. Solutions based on satellite altimetry and the input-output method run for the entire record, 78
roughly twice the duration of the gravimetry time series. Although most (59 %) estimates fall within 79
one standard deviation of the technique-dependent mean, a few (6 %) depart by more than three. 80
At the Antarctic Peninsula, the 25-year average rate of ice sheet mass balance is -20 ± 15 Gt/yr, with 81
a ~15 Gt/yr increase in losses since 2000. The strongest signal and trend has occurred in West 82
Antarctica, where rates of mass loss rise from 53 ± 29 Gt/yr to 159 ± 26 Gt/yr between the first and 83
final 5 years of our survey, with the largest increase occurring during the late 2000’s when ice 84
discharge from the Amundsen Sea sector accelerated 34. Both of these regional losses are driven by 85
reductions in the thickness and extent of floating ice shelves, which has triggering retreat, 86
acceleration, and drawdown of marine terminating glaciers 35. The least certain result is in East 87
Antarctica, where the average 25-year mass trend is 5 ± 46 Gt/yr. Overall, the Antarctic ice sheet lost 88
2720 ± 1390 Gt of ice between 1992 and 2017, an average rate of 109 ± 56 Gt/yr. 89
Knowledge of the ice sheet surface mass balance is an essential component of the input-output 90
method, which subtracts solid ice discharge from net snow accumulation, and also aids 91
interpretation of mass trends derived from satellite altimetry and gravimetry. Snowfall is the major 92
driver of temporal and spatial variability in Antarctic ice sheet surface mass change 36,37. Although 93
locally important, spatially integrated sublimation and meltwater runoff are typically one to two 94
orders of magnitude smaller, respectively. In the absence of observation-based maps, Antarctic ice 95
sheet surface mass balance is usually taken from atmospheric models, evaluated with in-situ and 96
remotely-sensed observations 15,38-41. To assess Antarctic surface mass balance, we compared two 97
global reanalysis products (JRA55 and ERA-Interim) and two regional climate models (RACMO2 and 98
MARv3.6)(see Methods). ERA-Interim is usually regarded as the best performing reanalysis product 99
over Antarctica, albeit with a dry bias in the interior and overestimated rain fraction 40,42,43. Spatially 100
averaged accumulation rates peak at the Antarctic Peninsula, and are ~3 and ~7 times lower in West 101
and East Antarctica, respectively (Extended Data Figure 2 and Extended Data Figure 3). Compared to 102
the all-model average surface mass balance of 1994 Gt/yr, the regional climate models have 4.7% 103
higher and the reanalyses 7% lower values. These differences can be attributed to the higher 104
resolution of the regional models, which resolve the steep coastal precipitation gradients in greater 105
detail, and also their improved representation of polar processes. The temporal variability of all 106
products is similar, and they all agree on the absence of an ice sheet wide trend in surface mass 107
balance over the period 1979 to 2017, implying that recent Antarctic ice sheet mass loss is 108
dominated by increased solid ice discharge into the ocean. 109
Gravimetric estimates of mass change are strongly influenced by the method used to correct for
110
glacial isostatic adjustment (GIA)16. In this study, six different GIA models were used for this purpose
111
22,25,27,31,32,44. We also assessed nine continent-wide forward-model and two regional model
112
simulations to better understand uncertainties in the GIA signal itself, and we reprocessed the
113
gravimetry estimates of mass balance using just the W12a 27 and IJ05_R2 32 GIA models for
114
comparison with earlier work18 (see Methods). The net gravitational effect of GIA across Antarctica is
115
positive, and the mean and standard deviation of the continent-wide GIA models (54 ± 18 Gt/yr) is 116
very close to that of W12a (56 ± 27 Gt/yr) and IJ05_R2 (55 ± 13 Gt/yr). The narrow spread likely 117
reflects the difficulty of quantifying the timing and extent of past ice sheet change, and the absence 118
of lateral variations in Earth rheology within some models 45. In areas where GIA is a significant
119
component of the regional mass change, such as the Amundsen, Ross and Filchner-Ronne sectors of
120
West Antarctica (see Extended Data Figure 4), models predict the greatest uplift rates (5 to 7 mm/yr
121
on average) but also the greatest variability (e.g. standard deviation > 10 mm/yr in the Amundsen
122
sector). Away from areas with large GIA signals there is low variance among the models and broad
123
agreement with GPS observations 46. Nevertheless, most models considered here do not account for
124
ice sheet change during the last few millennia, because it is poorly known. Inaccurate treatment of
125
low degree harmonics associated with the global GIA signal can also bias gravimetric mass balance
calculations 47. If the GIA signal includes a transient component associated with recent ice sheet
127
change this will bias mass trend estimates and should be accounted for in future work.
128
Improvements in ice sheet mass balance assessments are still possible. Airborne snow radar 48,49 is a 129
powerful tool for evaluating surface mass balance and firn compaction models over large spatial 130
(1000’s of km) and temporal (centennial) scales, in addition to the ice cores that have been 131
traditionally used50. Geological constraints on the ice sheet history 21 and GPS measurements of 132
contemporary uplift 46,51 allow GIA models to be scrutinised and calibrated. More of both these data 133
sets are needed, especially in East Antarctica. Given their apparent diversity, the spread of GIA and 134
surface mass balance models should be evaluated in concert with the satellite gravimetry, altimetry, 135
and velocity measurements. A reassessment of satellite measurements acquired during the 1990s 136
would address the imbalance that is present in the current record. Alternative techniques (e.g. 52) for 137
the combination of satellite data sets should be explored, and satellite measurements with common 138
temporal sampling should be contrasted. The ice sheet mass balance record should now be 139
separated into the contributions due to short-term fluctuations in surface mass balance and longer-140
term trends in glacier ice. In addition to these obvious improvements, continued satellite 141
observations are, of course, essential. 142
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Supplementary Information
276
A table summarising the details of the satellite datasets is included as Supplementary Information 277
(Supplementary Information Table 1). 278
279
Acknowledgements
280
This work is an outcome of the ESA-NASA Ice Sheet Mass Balance Inter-comparison Exercise. Andrew 281
Shepherd was additionally supported by a Royal Society Wolfson Research Merit Award. 282
283
Author Contributions
284
Andrew Shepherd and Erik Ivins designed and led the study. Eric Rignot, Ben Smith, Michiel van den 285
Broeke, Isabella Velicogna, and Pippa Whitehouse led the input-output, altimetry, surface mass 286
balance, gravimetry, and glacial isostatic adjustment experiments, respectively. Gorka Moyano and 287
Mark Pattle performed the data collation and analysis. Andrew Shepherd, Erik Ivins, Kate Briggs, 288
Gerhard Krinner, Martin Horwath, Ian Joughin, Hannes Konrad, Malcolm McMillan, Jeremie 289
Mouginot, Sophie Nowicki, Inès Otosaka, Mark Pattle, Tony Payne, Eric Rignot, Ingo Sasgen, Ted 290
Scambos, Nicole Schlegel, Tom Slater, Ben Smith, Isabella Velicogna, Melchior van Wessem, and 291
Pippa Whitehouse wrote and edited the manuscript. All authors participated in the data 292
interpretation and commented on the manuscript. 293
294
Author Information
295
Reprints and permissions information is available at www.nature.com/reprints. The authors declare 296
no competing interests. Correspondence and requests for materials should be addressed to 297
299 Tables 300 Region 1992-1997 (Gt/year) 1997-2002 (Gt/year) 2002-2007 (Gt/year) 2007-2012 (Gt/year) 2012-2017 (Gt/year) 1992-2011 (Gt/year) 1992-2017 (Gt/year) EAIS 11 ± 58 8 ± 56 12 ± 43 23 ± 38 -28 ± 30 13 ± 50 5 ± 46 WAIS -53 ± 29 -41 ± 28 -65 ± 27 -148 ± 27 -159 ± 26 -73 ± 28 -94 ± 27 APIS -7 ± 13 -6 ± 13 -20 ± 15 -35 ± 17 -33 ± 16 -16 ± 14 -20 ± 15 AIS -49 ± 67 -38 ± 64 -73 ± 53 -160 ± 50 -219 ± 43 -76 ± 59 -109 ± 56
Table 1 | Rates of ice sheet mass change. Rates were determined from all satellite measurements
over various epochs for the East Antarctic (EAIS), West Antarctic (WAIS), Antarctic Peninsula (APIS) and Antarctic (AIS) ice sheets. The period 1992-2011 is included for comparison to a previous assessment 18, which reported mass balance estimates of 14 ± 43 Gt/yr for the EAIS, -65 ± 26 Gt/yr for the WAIS, -20 ± 14 Gt/yr for the APIS, and -71 ± 53 Gt/yr for the AIS. The small differences in our updated estimates are due to increases in the datasets used.
301
Figure Legends
302
Figure 1. Antarctic ice sheet mass balance. Rate of mass change of the Antarctic Peninsula (a), West
303
Antarctic Ice Sheet (b), and East Antarctic Ice Sheet (c) as determined from satellite altimetry (red), 304
input-output (blue), and gravimetry (green) observations and an average of estimates across each 305
class of measurement technique (black) The estimated one-, two-, and three-sigma range of the 306
class average are shaded in dark, mid, and light grey, respectively, and the number of individual 307
mass balance estimates collated at each epoch is shown along the top of each chart. 308
309
Figure 2. Cumulative Antarctic ice sheet mass change. Cumulative ice sheet mass changes (solid
310
lines) are determined from the integral of the measurement class average (Figure 1) for each ice 311
sheet. The estimated one-sigma uncertainty of the cumulative change is shaded. 312 313 Methods 314
Data
315We analyse five groups of data; mass balance estimates determined from satellite altimetry, 316
gravimetry, and the input-output method, and model estimates of surface mass balance and glacial 317
isostatic adjustment. The data sets are computed using common spatial and temporal domains to 318
facilitate their aggregation, and according to methods report in the peer reviewed literature. In total 319
24 individual mass balance data sets were included. The data include 25 years of satellite radar 320
altimeter measurements, 24 years of satellite input-output method measurements, and 14 years of 321
satellite gravimetry measurements (Extended Data Figure 1). Among these data are estimates of ice 322
sheet mass balance for each ice sheet derived from each satellite technique. In comparison to the 323
first IMBIE assessment, new satellite missions, updated methodologies and improvements in 324
geophysical corrections have contributed to an increase in the quantity, duration and overlap period 325
of data used in this second assessment. In addition, two new experiment groups have assessed 11 326
Glacial Isostatic Adjustment models and 4 Surface Mass Balance models. The complete list of data 327
sets can be found in Supplementary Information Table 1. 328
Drainage Basins
329
In this assessment, we analyse mass trends using two sets of ice sheet drainage basin (Extended 330
Data Figure 2), to ensure consistency with those used in the first IMBIE assessment 18, and to 331
evaluate an updated definition tailored towards input-output method assessments. The first 332
drainage basin set was delineated using surface elevation maps derived from ICESat-1 based on the 333
provenance of the ice, and includes 27 basins 3. The second set are updated to consider other factors 334
such as the direction of ice flow, and include 18 basins in Antarctica 2,20. To assess the effect of the 335
different basin outline sets on the estimates of ice sheet mass balance, we compared mass balance 336
determinations between the two delineations of ice sheet drainage basins. This evaluation was 337
facilitated by seven estimates (altimetry or gravimetry) determined using both drainage basin sets. 338
At the scale of the major ice sheet divisions, the delineations produce similar total extents. By far the 339
largest differences occur in the delineation (or definition) of East and West Antarctica, due to 340
differences in the position of the ice divide separating them. Within these regions, the root mean-341
square difference between 26 pairs of ice sheet mass balance estimates computed using the two 342
drainage basin sets is 8.7 Gt/yr. This difference is small in comparison to the certainty of individual 343
ice sheet mass balance assessments. 344
Computing Rates of Mass Change
345
The raw satellite mass balance data are either time-series of either relative mass change, ∆M(t), or 346
the rate of mass change, dM(t)/dt, plus their associated uncertainty, integrated over at least one of 347
the ice sheet regions defined in the standard drainage basin sets. In the case of ∆M(t), the time 348
series represents the change in mass through time relative to some nominal reference value. The 349
duration and sampling frequency of the series was not restricted. In practice, few mass time-350
series were of ∆M(t) and dM(t)/dt. Because the inter-comparison exercise is based on comparing 351
and aggregating rates of mass change, dM(t)/dt, a common solution was implemented to derive 352
dM(t)/dt values from data sets that comprised ∆M(t) only. Each ∆M(t) time series was used to 353
generate a time-varying estimate of the rate of mass change, d(∆M(t))/dt=dM(t)/dt, and an estimate 354
of the associated uncertainty, using a consistent approach. Time varying rates of mass change were 355
computed by applying a sliding fixed-period window to the ∆M(t) time series. At each node, defined 356
by the sampling period of the input time series, dM(t)/dt and its standard error, σdM(t)/dt, were 357
estimated by fitting a linear trend to data within the window using a weighted least-squares 358
approach, with each point weighted by its respective error variance, σ∆M(t)2. The regression error, 359
σdM(t)/dt, incorporates measurement errors and model structural error due to any variability that 360
deviates from linear trends in ice mass, and may be a conservative estimate in locations where such 361
deviation is present. Time series of dM(t)/dt computed using this approach were truncated by half 362
the moving average window period. When integrated, the dM(t)/dt time series correspond to a low-363
pass filtered version of the original ∆M(t) time-series. Although the current linear regression 364
assumes uncertainties are uncorrelated, the smoothing we apply during the trend calculation does 365
cause data points to be correlated during a number of epochs beyond the sliding window. 366
Surface Mass Balance
367
Ice sheet surface mass balance (SMB) comprises a variety of processes governed by the interaction 368
of the superficial snow and firn layer with the atmosphere. A direct mass exchange occurs via 369
precipitation and surface sublimation. Snow drift and the formation of meltwater and its subsequent 370
refreezing or retention redistribute mass spatially or lead to further mass loss via erosion and 371
sublimation, or runoff. In this assessment, a range of SMB products are compared. Four SMB model 372
solutions were considered for Antarctica (Extended Data Table 1); two regional models - RACMO2.3 373
41 and MARv3.6 53 - and two global reanalysis products - JRA55 54 and ERA-Interim 55. The two 374
regional climate models agree well in terms of their spatially integrated SMB, apart from the 375
Peninsula where there is an offset of about 10 Gt/month between them (Extended Data Figure 3). 376
However, the reanalysis data underestimated the average SMB compared to the regional climate 377
models by 200 to 350 Gt/yr. The SMB assessment illustrates that products of similar class (climate 378
models, reanalysis product) agree well, suggesting that groupings of their output may be 379
appropriate. Model resolution is, however, found to be an important factor when estimating SMB 380
and its components, as respective contributions where only the spatial resolution differed yield 381
regional differences. 382
Glacial Isostatic Adjustment
383
Glacial isostatic adjustment (GIA) is the delayed response of the solid Earth to changes in time-384
variable surface loading through the growth and decay of ice sheets, and associated changes in sea 385
level. Because GIA contributes to changes in the ice sheet surface elevation and gravity field, it must 386
be accounted for in measurements of the change in elevation and gravity for the purpose of isolating 387
the contribution solely caused by ice sheet imbalance. In this assessment, we compare different 388
solutions derived from continuum-mechanical forward modelling to inform the interpretation of the 389
satellite altimetry and gravimetry data which depend on the correction, and to advise future 390
assessment exercises. Twelve GIA contributions were received covering Antarctica (Extended Data 391
Table 2), ten of which are global 23-30,32 and two of which are regional models 33. As a broad array of 392
data may be used to constrain GIA forward models, we anticipate spread in the predictions. 393
In the present analysis, the degree of similarity between the various GIA model solutions is assessed. 394
Areas of enhanced present-day vertical surface motion and (dis-)agreement between contributions 395
have been identified by averaging the uplift rates over the contributions and computing respective 396
standard deviations (Extended Data Figure 4). In some cases, it was necessary to estimate the GIA 397
contribution to gravimetric mass trends; this was done using common geographical masks and 398
truncation, and a standardized treatment of low degree harmonics. In Antarctica, the Amundsen Sea 399
sector and the regions covered by the Ross and Filchner Ronne Ice Shelves stand out as having both 400
high uplift rates (5-7 mm/yr on average) and high variability in uplift rates (peaking at >10 mm/yr 401
standard deviation in the Amundsen sector) among the models considered. Elsewhere in coastal 402
regions, uplift occurs at more moderate rates (~2 mm/yr on average), and the interior of East 403
Antarctica exhibits slow subsidence. In these regions, the average signal is accompanied by relatively 404
low variance among the GIA models (0-1.5 mm/yr standard deviation). None of the models fully 405
capture portions of the uplift that are observed to be very large (e.g. 56), hence, we can anticipate a 406
bias toward low values for the GIA correction averaged over such regions. In areas of low mantle 407
viscosity, however, such as part of the WAIS, the LGM-related GIA signal may be over-predicted, and 408
it is not clear whether a bias exists at the continental scale. 409
Differences between the model predictions arise for a variety of additional reasons. Technical 410
differences in the modelling approach, for example relating to the consideration of self-gravitation, 411
ocean loading, rotational feedback, and compressibility, will be most important at the global scale, 412
but may explain only small differences among the regional models. Differing treatment of ice/ocean 413
loading in regions that have experienced marine-based grounding line retreat during the last glacial 414
cycle may explain the differences in model predictions for the ICE_6G_C/VM5a combination (see 415
Supplementary Information Table 1). Some small differences should be expected when comparing 416
models that use spherical harmonic and finite element approaches. Looking beyond consideration of 417
the model physics, larger differences arise due to the various approaches used to determine the two 418
principal unknowns associated with forward modelling of GIA, namely ice history and Earth 419
rheology. There is no generally accepted ‘best approach’ to determining these inputs, and indeed 420
useful advances can be made by comparing the results of complementary approaches. In the models 421
considered here, approaches to determining the ice history include dynamical ice-sheet modelling, 422
coupled ice-sheet–GIA modelling, tuning to fit geodetic constraints, tuning to fit geological 423
constraints, and use of direct observations of historical ice sheet change. When defining the 424
rheological properties of the solid Earth, most studies have opted to use a Maxwell rheology to 425
define a radially-symmetric Earth, but the use of a power-law rheology and/or fully-3D Earth model 426
to capture the spatial complexity of mantle properties is increasingly popular. An intermediate 427
approach used in many of the data sets included in this study has been to develop a regional GIA 428
model that reflects local Earth structure. Such models can be tuned, albeit imperfectly, to provide as 429
accurate a representation of GIA in that region as is possible. However, it remains a difficult and 430
important challenge to incorporate these regional studies into a global framework. Finally, although 431
four of the considered GIA models do provide a measure of uncertainty, and a number of studies 432
have used an ensemble modelling approach 24,30, an important future goal for the GIA modelling 433
community is the inclusion of robust error estimates for all model predictions. 434
To compare the GIA models, Stokes coefficients relating to their gravitational signal were used to 435
determine the approximate magnitude of the effect of applying each correction to GRACE data 436
(Extended Data Table 2). This is a preliminary assessment, because the effect of applying a GIA 437
correction depends also on the methods used to process the GRACE data. Moreover, an agreement 438
on the modelling of the rational feedbacks has so far not been reached within the GIA community, 439
leading to a large spread in the modeled degree 2 coefficients and possibly a strong bias when a 440
correction is applied that is inconsistent with the GRACE observations (up to ca. 40 Gt/yr). In 441
addition, none of the current GIA data sets include estimates of the GIA-induced geocenter motion 442
(degree 1 coefficients). Therefore, we omit degree 1 and 2 coefficients in this assessment of the GIA-443
induced apparent mass change at this stage. From models representing GIA in Antarctic only, we 444
estimate that this omission may change the apparent mass change value by up to 20 %, which is 445
currently not included in the GIA error budget. There is relatively good agreement between the ten 446
models that cover all of Antarctica (Extended Data Table 2); the estimated GIA contribution ranges 447
from +12 to +81 Gt/yr, and the mean value is 56 Gt/yr. Although van der Wal et al. is a notable 448
outlier, this is the only solution to account for 3D variations in Earth rheology, and it will be 449
interesting to compare this result with other such models that are in development. It is important to 450
note that two of the GIA models are regional (Nield, Barletta); although they cannot be directly 451
compared with the continental-scale models, the magnitude of their signals is nonetheless included 452
for interest. 453
Mass Balance Intra-comparison
454
First, we compare estimates of mass change within each of the three geodetic technique experiment 455
groups, separately, to assess the degree to which results from common techniques concur and to 456
then arrive at individual, aggregated estimates of mass change derived from each technique alone. 457
In each case we compare estimated rates of mass change derived from a common technique over a 458
common geographical region and over the full period of the respective data sets. Where data sets 459
were computed using both drainage basin definitions, the arithmetic mean of the two estimates is 460
presented. This is justified because the choice of drainage basin set has a very small (<10 Gt/yr) 461
impact on estimates of mass balance at the ice sheet scale and even less at the regional scale. Within 462
each experiment group, we perform an unweighted average of all individual data to obtain a single 463
estimate of the rate of mass change per ice sheet for each geodetic technique In a few cases, it was 464
not possible to determine time-varying rates of mass change from individual estimates, because only 465
constant rates of mass change and constant cumulative mass changes were supplied. Although the 466
effect of averaging these data sets with time-varying solutions is to dampen the temporal variability 467
present within the series of finer resolution, they are retained for completeness. We estimate the 468
uncertainty of the average mass trends emerging from each experiment group as the average of the 469
errors associated with each individual estimate at each epoch. 470
To aid comparison, we (i) computed time-variable rates of mass change and their associated 471
uncertainty over successive 36-month periods stepped in 1-month intervals from time-varying 472
cumulative mass changes, and we then (ii) average rates of mass change over 1-year periods to 473
remove signals associated with seasonal cycles. Time-varying rates of mass change are truncated at 474
the start and end of each series to reflect the half-width of the time interval over which rates are 475
computed, though this period is recovered on integration to cumulative mass changes. The extent to 476
which we are able to analyse differences in mass balance solutions emerging from common satellite 477
approaches is limited by the mismatch in temporal resolution of the individual datasets, which 478
makes methodological and sampling differences difficult to separate. 479
Gravimetry Mass Balance Intra-comparison
480
Within the gravimetry experiment group, 15 estimates of mass balance derived from the GRACE 481
satellites were assessed, in entirety spanning the period July 2002 to September 2016. Of these 482
datasets, four (Luthcke, Moore, Save, Wiese) are derived with direct imposition of the GRACE Level-1 483
K-band range-data 57-60. These impositions result in 4 different, and quite independently derived, 484
mascon approaches. Other methods often refer to ‘mascon analysis’, but are conducted on post-485
spherical harmonic (post-SH) expansions and without imposing the Level 1 K-band range data. We 486
distinguish the later methods, referring to them as ‘post-SH mascons’. Eleven contributions are 487
derived from monthly spherical harmonic solutions of the global gravity field using somewhat 488
different approaches 61-67, which can be loosely classified as region integration approaches for 3 489
contributions (Blazquez, Groh, Horvath), post-SH mascon approaches for 4 contributions (Bonin, 490
Forsberg, Schrama, Velicogna). Forward-modelling is also an approach used in two contributions 491
(Wouters, Seo) and this essentially involves modelling of mass change with iterative comparison to 492
the GRACE-derived signal. One estimate (Harig) uses Slepian functions 68. One esimate (Rietbroek) 493
uses a hybrid approach involving satellite altimetry that does not fall within the above categories 69; 494
although these results are excluded from our gravimetry-only average, we present them alongside 495
the gravimetry-only results for comparison. No restrictions were imposed on the choice of glacial 496
isostatic adjustment correction, and among the GRACE solutions we consider six different models
497
were used for this purpose 22,25,27,31,32,44. We did, however, assess a wider set of nine continent-wide
498
forward models and two regional models to better understand uncertainties in the GIA signal itself.
499
In total, there were 15 estimates of mass balance for each of the APIS, WAIS, and EAIS. All were 500
time-varying cumulative mass change solutions - the primary GRACE observable - and we computed 501
time-varying rates of mass change from these data. Combining all of the individual mass balance 502
estimates, the effective (average) temporal resolution of the aggregated solution is 1 year. Further 503
details of the gravimetry data sets and methods are included in Supplementary Information Table 1. 504
Extended Data Figure 5 shows a comparison of rates of mass change obtained from all gravimetry 505
mass balance solutions, calculated over the three main ice sheet regions. At individual epochs, 506
differences between time-varying rates of mass change are generally smaller than 50 Gt/yr in each 507
ice sheet region, and typically fall in the range 10 to 20 Gt/yr. Over the full period of the data, 508
individual rates of mass balance for the APIS, WAIS, and EAIS vary between -80 to +10, -260 to -20, 509
and -120 to +200 Gt/yr, respectively. Considering all of the gravimetry data (Extended Data Table 3); 510
the standard deviation of mass trends estimated during the period 2005 to 2015 is less than 24 Gt/yr 511
in all three ice sheet regions, with the largest spread occurring in the EAIS. In all three ice sheet 512
regions, the spread of individual mass balance estimates is well represented by the mean 513
considering the uncertainties of the individual and aggregated datasets. 514
Altimetry Mass Balance Intra-comparison
515
We assessed 7 radar and laser altimetry derived estimates of Antarctic ice sheet mass balance data 516
sets, in entirety spanning the period April 1992 to July 2017. In total, 6 estimates of mass change 517
were for the APIS, 7 for the EAIS, and 7 for the WAIS. Of these, 4 included data from radar altimetry, 518
and 6 from laser altimetry. A variety of different techniques were employed to arrive at elevation 519
and mass trends 70-76. Only 2 of the altimetry data sets were time-series of cumulative mass change, 520
from which we computed time-varying rates of mass change. The remaining altimetry data sets were 521
constant rates of mass change, which appear in our altimetry average as time-invariant solutions. 522
The period over which altimetry rates of mass change were computed ranged from 2 to 24 years. In 523
consequence, the aggregated dataset has a temporal resolution that is lower than annual. Including 524
all individual mass balance data sets, the effective (average) temporal resolution of the aggregated 525
solution is 3.3 years. Further details of the altimetry data sets and methods are included in 526
Supplementary Information Table 1. 527
With a few exceptions, rates of mass change determined from radar and laser altimetry tend to 528
differ by less than 100 Gt/yr at all times in each ice sheet region (Extended Data Figure 5). The main 529
exceptions are in the EAIS, where one estimate (Zwally) reports mass trends that are ~100 Gt/yr 530
more positive than all others during the ERS and ICESat periods and the WAIS, where two estimates 531
(Zwally and Helm) report rates that are ~70 Gt/yr less negative than the others during the ICESat 532
period. Among the remaining data sets, the closest agreement occurs at the APIS, where mass 533
trends agree to within 30 Gt/yr at all times, and the poorest agreement occurs at the EAIS, where 534
mass trends depart by up to 100 Gt/yr. The largest differences are among datasets that are constant 535
in time during periods where rapid changes in mass balance occur in the annually resolved time 536
series, suggesting that a proportion of the difference is due to their poor temporal resolution. Mass 537
balance solutions from the relatively short (six-year) ICESat mission also appear to show larger 538
spreads compared to those determined from longer (decade-scale) radar-altimetry missions. This 539
larger spread is due in part to differences in the bias-correction models applied to ICESat data 75,77-79 540
and in part to the large influence of firn densification on altimetry measurements over short periods, 541
which have been corrected for using different models. Firn-densification models are generally not 542
applied to mass balance solutions determined from radar altimetry. Further analysis of the 543
corrections for bias between ICESat campaigns and firn compaction is required to establish the 544
significance of the differences and to reduce their collective uncertainty. Comparing rates of mass 545
change (Extended Data Table 3), the average standard deviation of all mass trends at each epoch 546
over the common period 2005 to 2015 is less than 54 Gt/yr in all four ice sheet regions. The largest 547
spread among the individual values occurs in the EAIS. Other than this sector, all of the individual 548
estimates lie close to the ensemble average, considering the respective uncertainty of the 549
measurements. 550
Input-Output Method Intra-comparison
551
Although the input-output method is a most direct measure of changing in mass fluxes, a main 552
difficulty is that it must differ two large numbers - one for annual SMB and the other for discharge 553
plus grounding line migrations - and deal appropriately with the error budgets of both, in order to 554
assess mass balance. A consequence of this complexity is that few input-output method data sets 555
exist at the ice sheet scale. In this assessment, we collate just two input-output data sets, both based 556
on the same method 80 - far fewer than were considered for altimetry and gravimetry. The first 557
input-output method dataset spans the period 1992 to 2010 18. The second input-output method 558
dataset is limited to the period 2002 to 2016. The same SMB model was used in both assessments - 559
RACMO2.3. Further details of the input-output method data sets and methods are included in 560
Supplementary Information Table 1. 561
We compared the two input-output method data sets during the period 2002 to 2010 when they 562
overlap (Extended Data Table 3). The smallest differences (up to 30 Gt/yr) arise in the APIS and the 563
WAIS, and the largest differences (up to 70 Gt/yr) occur at the EAIS. In all cases, the average 564
difference between estimates of mass balance derived from each dataset is comparable to the 565
estimated certainty. Including both datasets, rates of mass balance over the period 1992 to 2016 for 566
the APIS, WAIS and EAIS fall in the range -125 to +25 Gt/yr, -300 to +100 Gt/yr and -200 to +200 567
Gt/yr, respectively (Extended Data Figure 5). The origin of the differences between the two datasets 568
requires further investigation. 569
Ice Sheet Mass Balance Inter-comparison
570
To assess the degree to which the satellite techniques concur, we used the aggregated time series 571
emerging from each geodetic technique experiment group to compute changes in ice sheet mass 572
balance within common geographical regions and over a common interval of time (the overlap 573
period). The aggregated time series were calculated as the arithmetic mean of all available rates of 574
ice sheet mass balance derived from the same satellite technique at each available epoch. We used 575
the individual ice sheets and their integrals as common geographical regions. The maximum duration 576
of the overlap period is limited to the 14-year interval when all three satellite techniques were 577
optimally operational, namely 2002 to 2016. However, we also considered the availability of mass 578
balance data sets, which leads us to select the period 2003 to 2010 as the optimal interval (see 579
Figure 1). When the aggregated mass balance data emerging from all three experiment groups are 580
degraded to a common temporal resolution of 36 months, the time-series are on average well 581
correlated (0.5<r2<0.9) at the APIS and WAIS. At the EAIS, however, the aggregated altimetry mass 582
balance time series are poorly correlated (r2<0.1) in time with the aggregated gravimetry and input-583
output method data. Possible explanations for this include the relatively high short-term variability 584
in mass fluctuations in this region, the relatively low trend in mass, and the heterogeneous temporal 585
resolution of the aggregated altimetry data set. Over longer periods, marked increases in the rate of 586
mass loss from the WAIS are also recorded in all three satellite data sets. 587
Because the comparison period is long in relation to the timescales over which surface mass balance 588
fluctuations typically occur, their potential impact on the overall inter-comparison is reduced. The 589
closest agreement between individual estimates of ice sheet mass balance occurs at the APIS and 590
the WAIS, where the standard deviation across all techniques falls between 15 and 41 Gt/yr 591
(Extended Data Table 4). The greatest departure occurs at the EAIS, where the input-output method 592
and gravimetry estimates of mass balance differ by ~80 Gt/yr, and where the standard deviation of 593
all three estimates is ~40 Gt/yr. This high degree of variance is expected due to the relatively large 594
size of the region, small amplitude of signals and poor independent controls on coastal SMB. When 595
compared to the mean, there are no significant differences between estimates of ice sheet mass 596
balance determined from the individual satellite techniques and, in contrast to the first assessment, 597
this finding also holds at continental and global scale. We conclude, therefore, that estimates of 598
mass balance determined from independent geodetic techniques agree when compared to their 599
respective uncertainties. 600
Several noteworthy patterns in the distribution of mass balance estimates determined during the 601
overlap period (2003 to 2010) merit further discussion. Estimates of mass balance derived from 602
satellite altimetry and gravimetry are agree to within 15 Gt/yr, on average, and with the mean of all 603
three techniques, in all ice sheet regions. In contrast, estimates of mass balance determined from 604
the input-output method are 55 Gt/yr more negative, on average, than the mean in all ice sheet 605
regions. However, despite the bias, the input-output method estimates remain in agreement 606
because their estimated uncertainty is relatively large (approximately three times larger than that of 607
the other techniques). A more detailed analysis of the primary and ancillary datasets is required to 608
establish whether this bias is significant or systematic. 609
Ice Sheet Mass Balance Integration
610
We combined estimates of ice-sheet mass balance derived from each geodetic technique 611
experiment group to produce a single, reconciled assessment, following the same approach as the 612
first assessment exercise. This was computed as the arithmetic mean of the average rates of mass 613
change derived from each experiment group, within the regions of interest and at the time periods 614
for which the experiment group mass trends were determined. We estimated the uncertainty of the 615
mass balance data using the following approach. Within each experiment group, the uncertainty of 616
mass trends was estimated as the average of the errors associated with each individual estimate. 617
The uncertainty of reconciled rates of mass change (e.g. Table 1) was estimated as the root mean 618
square of the uncertainties associated with mass trends emerging from each experiment group. 619
When summing mass trends of multiple ice sheets, the combined uncertainty was estimated as the 620
root sum square of the uncertainties for each region. Finally, to estimate the cumulative uncertainty 621
of mass changes over time, we weighted the annual uncertainty by 1/√n, where n is the number of 622
years elapsed relative to the start of each time series, and then summed the weighted annual 623
uncertainties over time 81. 624
Across the full 25-year survey, the average rates of mass balance of the AIS was -109 ± 56 (Table 1). 625
To investigate inter-annual variability, we also calculated mass trends during successive 5-year 626
intervals. While the APIS and WAIS each lost mass throughout the entire survey period, the EAIS 627
experienced alternate periods of mass loss and mass gain, likely driven by inter-annual fluctuations 628
in SMB. The rate of mass loss from the WAIS has increased over time due to accelerated ice 629
discharge in the Amundsen Sea sector 34,48,74,82-84. The most significant rise – a twofold increase in the 630
rate of ice loss - occurred between the periods 2002-2007 and 2007-2012 (Table 1). Overall, the 631
WAIS accounts for the vast majority of ice mass losses from Antarctica. At the APIS, rates of ice mass 632
loss since the early 2000’s are notably higher than during the previous decade, consistent with 633
observations of surface lowering 72,74 and increased ice flow in southerly glacier catchments 85. The 634
approximate state of balance of the wider EAIS suggests that the reported dynamic thinning of the 635
Totten and Cook glaciers 86,87 has been offset by accumulation gains elsewhere 88. 636
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